Experimental Evidence of Critical Sensitivity in Catastrophe

The paper presents an experimental study on critical sensitivity in rocks. Critical sensitivity means that the response of a system to external controlling variable may become significantly sensitive as the system approaches its catastrophic rupture point. It is found that the sensitivities measured by responses on three scales (sample scale, locally macroscopic scales and mesoscopic scale) display increase prior to catastrophic transition point. These experimental results do support the concept that critical sensitivity might be a common precursory feature of catastrophe. Furthermore, our previous theoretical model is extended to explore the fluctuations in critical sensitivity in the rock tests.     

Damage Localization,Sensitivity of Energy Release and the Catastrophe Transition

-- Large earthquakes can be viewed as catastrophic ruptures in the earth's crust. There are two common features prior to the catastrophe transition in heterogeneous media. One is damage localization and the other is critical sensitivity; both of which are related to a cascade of damage coalescence. In this paper, in an attempt to reveal the physics underlying the catastrophe transition, analytic analysis based on mean-field approximation of a heterogeneous medium as well as numerical simulations using a network model are presented. Both the emergence of damage localization and the sensitivity of energy release are examined to explore the inherent statistical precursors prior to the eventual catastrophic rupture. Emergence of damage localization, as predicted by the mean-field analysis, is consistent with observations of the evolution of damage patterns. It is confirmed that precursors can be extracted from the time-series of energy release according to its sensitivity to increasing crustal stress. As a major result, present research indicates that the catastrophe transition and the critical point hypothesis (CPH) of earthquakes are interrelated. The results suggest there may be two cross-checking precursors of large earthquakes: damage localization and critical sensitivity.     

Critical Sensitivity in Driven Nonlinear Threshold Systems

— Rupture in heterogeneous brittle media, including earthquakes, can be regarded as complicated phenomena in driven nonlinear threshold systems. It displays catastrophe transition and sample-specificity, which results in difficulty of rupture prediction. Our numerical simulations indicate that critical sensitivity might be a common precursor of catastrophe transition and thus give a clue to catastrophe prediction. In this paper we present an analytical examination of critical sensitivity in driven nonlinear threshold systems, based on mean field approximation and damage relaxation time model. The result suggests that critical sensitivity is in reality a common feature prior to catastrophe transition in driven nonlinear threshold systems, with disordered mesoscopic heterogeneity. This result seems to be supported by rock experiments.     

Simulation of the Transition of Earthquake Rupture from Quasi-static Growth to Dynamic Propagation

-- We have simulated a rupture transition from quasi-static growth to dynamic propagation using the boundary integral equation method. In order to make a physically reasonable model of earthquake cycle, we have to evaluate the dynamic rupture propagation in the context of quasi-static simulation. We used a snapshot of the stress distribution just before the earthquake in the quasi-static simulation. The resultant stress will be fed back to the quasi-static simulation. Since the quasi-static simulation used the slip-and time-dependent constitutive relation, the friction law itself evolves with time. Thus, we used the slip-weakening constitutive relation for dynamic rupture propagation consistent with that used for the quasi-static simulation. We modeled a San Andreas type strike-slip fault, in which two different size asperities existed.     

3-D Simulation of Earthquake Generation Cycles and Evolution of Fault Constitutitve Properties

--The earthquake generation cycle consists of tectonic loading, quasi-static rupture nucleation, dynamic rupture propagation and stop, and subsequent stress redistribution and fault restrengthening. From a macroscopic point of view, the entire process of earthquake generation cycles should be consistently described by a coupled nonlinear system of a slip-response function, a fault constitutive law and a driving force. On the basis of such a general idea, we constructed a realistic 3-D simulation model for earthquake generation cycles at a transcurrent plate boundary by combining the viscoelastic slip-response function derived for a two-layered elastic-viscoelastic structure model, the slip- and time-dependent fault constitutive law that has an inherent mechanism of fault restrengthening, and the steady relative plate motion as a driving force into a single closed system. With this model we numerically simulated the earthquake generation cycles repeated in a seismogenic region on a plate interface, and examined space-time changes in shear stress, slip deficits and fault constitutive properties during one complete cycle in detail. The occurrence of unstable dynamic slip brings about decrease both in fault strength and shear stress to a constant residual level. After the arrest of dynamic slip, the breakdown strength drop j†_p of fault is restored rapidly and the process of stress accumulation resumes in the seismogenic region. On the other hand, the restoration of the critical weakening displacement D_c proceeds gradually with time through the interseismic period. The restoration of D_c can be regarded as the macroscopic manifestation of the microscopic recovery process of fractal fault surface structure. Through numerical simulation with a multi-segmented fault model, we examined the effects of viscoelastic fault-to-fault interaction. The effect of transient viscoelastic stress transfer through the asthenosphere is significant as well as the direct effect of elastic stress transfer, and it possibly explains the time lag of the sequential occurrence of large events along a plate boundary.     

Stress Correlation Function Evolution in Lattice Solid Elasto-dynamic Models of Shear and Fracture Zones and Earthquake Prediction

--It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.     

Load-Unload Response Ratio and Accelerating Moment/Energy Release Critical Region Scaling and Earthquake Prediction

-- The main idea of the Load-Unload Response Ratio (LURR) is that when a system is stable, its response to loading corresponds to its response to unloading, whereas when the system is approaching an unstable state, the response to loading and unloading becomes quite different. High LURR values and observations of Accelerating Moment/Energy Release (AMR/AER) prior to large earthquakes have led different research groups to suggest intermediate-term earthquake prediction is possible and imply that the LURR and AMR/AER observations may have a similar physical origin. To study this possibility, we conducted a retrospective examination of several Australian and Chinese earthquakes with magnitudes ranging from 5.0 to 7.9, including Australia's deadly Newcastle earthquake and the devastating Tangshan earthquake. Both LURR values and best-fit power-law time-to-failure functions were computed using data within a range of distances from the epicenter. Like the best-fit power-law fits in AMR/AER, the LURR value was optimal using data within a certain epicentral distance implying a critical region for LURR. Furthermore, LURR critical region size scales with mainshock magnitude and is similar to the AMR/AER critical region size. These results suggest a common physical origin for both the AMR/AER and LURR observations. Further research may provide clues that yield an understanding of this mechanism and help lead to a solid foundation for intermediate-term earthquake prediction.     

历史大地震破裂区地震危险性的地震活动性定量分析——以南北地震带中北段为例

尽管地震空区理论在中长期地震预测中起着重要的作用,但大地震复发在时间上的丛集或非线性行为使得在中长期地震预测研究中依然需要同时考虑非地震空区的、历史地震破裂区的潜在大地震危险性。为了探索能基于观测资料分析的、鉴别历史地震破裂区(包括历史、史前地震破裂的地震空区)大地震复发危险性的技术方法,在南北地震带中北段挑选出8个具有不同离逝时间的历史大地震破裂区,分析这些破裂区现代地震活动性的量化特征,以初步探索判定潜在大地震危险性紧迫程度的地震活动性方法。结果表明,反映地震序列衰减状态的p值和反映地震活动率的a值与这些历史破裂区最晚大地震的离逝时间有较好的对应关系,但也有部分破裂区可能由于复杂的断层结构与运动性质,对应关系并不明确;反映构造应力积累状况的b值则难于反映离逝时间演化阶段的信息。b值的时间扫描结果显示,大部分历史破裂区的b值随时间演化平稳,但1879年甘肃武都8级地震破裂区的b值则表现为明显的涨落,并存在持续20年的降低趋势。对比分析认为,1933年四川茂县7.5级、1976年四川松潘—平武两次7.2级地震破裂区目前仍处于序列衰减期,不具备再次发生7级以上地震的背景;公元842年迭部7级地震破裂区北缘低b值的玛曲段比迭部段更具危险性;1879年武都8级地震破裂区的b值持续降低也可能反映该区处于新的一轮孕震期。     

基于断层运动和应力演化分析断层强震危险程度的研究进展

震间断层强震危险性研究是地震中长期预测中的基础科学问题, 其中断层运动及应力演化的研究对认识地震的孕育发生、 破裂过程具有重要意义, 为地震危险性分析提供科学依据。 本文首先回顾了震间断层运动模型的理论研究进展; 其次, 简略地回顾了断层不均匀性和断层摩擦定律的研究历程, 论述了确定摩擦参数、 圈定凹凸体的发展趋势与研究动态, 并阐述了基于断层不均匀性和断层摩擦定律的强震过程数值模拟的应用; 最后, 论述了基于断层运动和应力演化分析断层中长期强震危险程度的应用, 并叙述了与地震短期、 临震预测密切相关的断层运动成核过程。     

Simulation of the Load-Unload Response Ratio and Critical Sensitivity in the Lattice Solid Model

— The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.     

Phase Space Structure, Attractor Dimension, Lyapunov Exponent and Nonlinear Prediction from Earth’s Atmospheric Angular Momentum Time Series

--On a short time scale, Atmospheric Angular Momentum (AAM) has been demonstrated to be essentially the sole excitation source of LOD variations. The LOD variation, therefore, merely reflects the AAM variation (LOD as proxy for AAM). The study of the nonlinear nature of AAM variability (e.g., its orbital complexity, dimensionality and extreme sensitivity to the initial conditions) may provide a physical premise for theoretical modelling of the earth-atmosphere-ocean system. Analysis of the high quality of detailed daily LOD/AAM variations time series, spanning the period of 1962-1992, reveals a non-zero and low positive Lyapunov exponent value which suggests possible evidence of deterministic chaos in the underlying dynamics. Application of modern nonlinear prediction techniques capable of distinguishing chaos and random fractals to the data set, further support the above findings and render a predictive time limit of approximately 12-15 days. A low dimensional strange attractor and a low average Lyapunov exponent suggest a low level of unpredictability and stability in the system dynamics. It is argued here that a possible source of the raised entropy in LOD/AAM systems possibly stems from a conceivable nonlinear interaction between the seasonal cycle and inter- or intra-annual fluctuations due to thermodynamics properties of the atmosphere-ocean system.     

The aftershock dynamics of the Sumatra-Andaman earthquake

The aftershocks of the catastrophic Sumatra-Andaman earthquake of December 26, 2004 (M = 9.0) are analyzed in the general context of the theory of critical phenomena. The analysis relies on the idea that, according to this theory, critical transitions have two key properties. The first is that the intensity of the fluctuations in a dynamical system monotonically increases with the approach of the bifurcation point, so that at a certain time instant, a sufficiently strong internal pulse initiates the catastrophe. This transition can be treated as spontaneous. The second property is that the reactance of the dynamical system drastically increases on the approach of the bifurcation. Even a weak external perturbation in the near-threshold interval can result in a catastrophe. In this case, it is reasonable to refer to the critical transition as an induced transition. The aftershocks of the Sumatra-Andaman earthquake are likely to demonstrate the typical features of induced seismicity. First, the strongest aftershock (M = 7.2) occurred 3 h 20 min after the main shock. It could have probably been induced by the round-trip seismic echo. Second, it was found that the spectral density of the aftershock sequence significantly increases at about ～0.3 mHz, which is close to the frequency of the spheroidal mode ₀S₂. This suggests that the spheroidal oscillations of the Earth, which are excited by the main seismic shock, modulate the aftershock activity. Both hypotheses are supported by the analysis of the aftershocks of the Tohoku earthquake of March 11, 2011 (M = 9.0).     

On the Generation of ULF Magnetic Variations by Conductivity Fluctuations in a Fault Zone

v--vPrior to the October 18, 1989 Loma Prieta M_s 7.1 earthquake, Fraser-Smith et al. (1990) recorded a 10-100 fold increase in ultra-low frequency (ULF) magnetic fields near the earthquake epicenter. Several mechanisms for generation of these ULF fields by fluid flow in the earth have been advanced, but all appear to require unrealistic fluid velocities or hydraulic permeabilities to match the observations. As an alternative explanation, Merzer and Klemperer (1998) proposed that the increase in ULF magnetic fields could result from induced electric currents flowing in a fault-zone made temporarily much more electrically conductive by stress-induced reorganization of pore geometry. Using a numerical model we show that while this mechanism could produce a significant increase in ULF variations, mutual induction between the fault zone and the surrounding crust would probably limit the amplitude increase to levels well below those observed at Loma Prieta. We consider a variant on this quasi-static conductive fault zone model in which low frequency telluric currents are modulated by small higher frequency variations of bulk fault zone conductivity. We show that because the spectrum of natural EM variations is red, substantially larger relative increases in ULF magnetic fields could be produced by this mechanism with even small conductivity fluctuations at these frequencies. These variations would be easy to detect with a well-designed experiment, if they occurred. In principle this mechanism could explain the Loma Prieta ULF observations, however the magnitude of conductivity fluctuations that would be required to match the very large reported amplification factors still appears to be too large to be physically plausible.     

2013年4月20日四川芦山地震震源破裂过程反演初步结果

使用远场体波资料和有限断层方法快速反演获得了2013年4月12日芦山地震的震源破裂过程模型,并计算了震中区理论烈度分布.结果显示这次地震是发生在龙门山断裂带南端的一次M_w6.7级的逆冲型地震,最大滑动量159 cm,震中区烈度达Ⅷ-IX度(中国地震烈度表).这次地震的震源性质与汶川地震同为逆冲型破裂,主要破裂滑动发生在汶川地震后的库伦应力增加区域,表明汶川地震对这次地震有触发效应,在宏观上可视为汶川地震一次"迟到"的强余震.     

2008年汶川大地震中北川地区极重震害的物理机制研究

2008年汶川特大地震中北川地区受灾特别严重,而该地区远离汶川主震震中超过100多千米.尽管汶川地震发生已近10年,但这种不正常现象一直困扰着地学工作者,至今没有给出合理的解答.为此,本文利用有限单元方法模拟汶川地震的主要发震断裂带（即：映秀—北川断层）的自发破裂动力学过程.模型中,几乎平直的映秀—北川断裂带在高川地区发生拐折,形成高川右弯.模拟结果显示,破裂沿着映秀—北川断裂带向东北方向前行,当破裂前端到达高川右弯时,破裂形态发生剧烈变化,破裂传播速度由亚剪切破裂突然转化为超剪切破裂.与断层阶区促进超剪切破裂明显不同的是,这种超剪切破裂形态的转化不需要时间停顿.由于超剪切地震破裂的产生,破裂辐射的地震波发生相长干涉,形成马赫波,地震动被大大放大.计算给出的强地面运动峰值加速度在北川地区不仅数值高,而且高值区分布范围广,造成了北川地区的震害特别严重.模拟结果还表明,若高川右弯不存在（即映秀—北川断层面为平直）,则北川地区的断层不会形成超剪切破裂;如果高川右弯附近断层的不连续程度较大,则破裂会被终止;这些情况下,北川地区的震害都没有那么严重.所以,高川右弯的几何形状对于超剪切破裂的形成起着决定性作用,也是造成远离震中的北川地区震害特别严重的主要原因.因此,分析发震断层几何对于研究震源动力学过程及震害评估等有着非常重要的科学意义和实际应用价值.     

co-seismic coulomb stress changes and its influences on aftershock distribution and surrounding faults caused by 2014 ludian earthquake,yunnan

The studies of earthquake stress transfer and its influence on regional seismicity have found that earthquake occurrences are highly interactive and correlated rather than isolated and random in traditional point in recently years. A lot of phenomena in earthquake observations such as aftershock distribution, stress shadow, earthquake interaction and migration were well explained based on the theory of earthquake stress interaction. It is important that understanding the process of earthquake interaction could give an insight into the physical mechanism of earthquake cycle, and could help us assess the seismic hazard in future.It has long been recognized that regional stress accumulated by tectonic motion is released when earthquake occurs. When earthquakes occur, the accumulated stress does not vanish completely, but is redistributed through the process of stress transfer, and then the redistributed stress may trigger potential earthquakes. The increment of Coulomb failure stress loading in the certain regions may improve the seismic activities. By contrast, the decrement of Coulomb failure stress in the areas of stress shadow where the stress on faults may unload could lead to the decrement of seismic activities.On August 3, 2014, an M_S6.5 earthquake occurred in Zhaotong-Ludian region, Yunnan Province, China, killing and injuring hundreds of people. Therefore, it is critical to outline the areas with potential aftershocks before reconstruction and re-settlement so as to avoid future disasters. Based on the elastic dislocation theory and multi-layered lithospheric model, we calculate the co-stress changes caused by the Zhaotong-Ludian earthquakes to discuss its influences on aftershock distribution and surrounding faults. It is shown that the Coulomb stress changes based on the rupture in the NNW direction can explain better the aftershock distribution. It indicates that the NNW direction may represent the real rupture. The aftershocks mainly distribute in the regions with increased stress along main rupture and west to the rupture. In other regions with increased stress, the distributions of aftershock are rare which may indicate the low tectonic stress accumulation in these regions. The stress accumulation and corresponding seismic hazard on the southern part of Zhaotong Fault, Qiaojia segment of Zemuhe-Xiaojiang Fault and northeastern part of Lianfeng Fault are further increased by the Zhaotong-Ludian earthquake. We should pay special attention to the southern part of Zhaotong Fault where seismic activity is very high in recently years and the increment of Coulomb failure stress in this area is more than 0.1bar(0.1bar is the threshold of earthquake triggering). In order to make a more objective and comprehensive discussion, we calculate the sensitivity of the parameters such as effective coefficient of friction, the calculated depth and multilayered crustal model.     

应力扰动对地震周期和地震矩影响的数值模拟

利用二维有限元数值模型,结合断层滑移弱化摩擦准则对断层滑动规律以及应力扰动对其影响进行了研究．数值计算结果表明,在均匀应力分布情况下, 平面断层滑动显示出典型的特征地震规律,断层面上的应力扰动对断层滑动规律产生影响,压应力增加明显延迟地震的发生时间,并增加地震释放的能量．应力扰动发生在地震破裂临界区时的影响比在震前滑移区时的影响显著．当发生在地震滑移区时,若应力扰动足够大,则压应力增大会造成地震发生时部分动力断层被暂时锁住,使得地震释放的能量变小,但可增加后续地震的能量; 而压应力减小则可导致地震规律产生更加复杂的变化,会即时触发地震．如果应力扰动发生在一个地震周期的早期,则触发的地震较小,但可导致随后的地震提前发生; 如果应力扰动发生在一个地震周期的后期,则会触发大地震．当应力扰动位于震前滑移区或破裂临界区时,小的扰动也可能产生类似的效果．应力扰动产生越晚,这种影响也越明显．应力扰动发生在破裂临界区的影响最明显．应力扰动的影响一般主要集中在应力发生扰动后的1—2个地震周期内．后续地震基本恢复无应力扰动时的特征地震规律．      

Combined GPS and InSAR Models of Postseismic Deformation from the Northridge Earthquake

--Models of combined Global Positioning System (GPS) and Interferometric Synthetic Aperture Radar (InSAR) data collected in the region of the Northridge earthquake indicate that significant afterslip on the main fault occurred following the earthquake. Additional shallow deformation occurred to the west of the main rupture plane. Both data sets are consistent with logarithmic time-dependent behavior following the earthquake indicative of afterslip rather than postseismic relaxation. Aftershocks account for only about 10% of the postseismic motion. The two data sets are complimentary in determining the postseismic processes. Fault afterslip and shallow deformation dominate the deformation field in the two years following the earthquake. Lower crustal deformation may play an important role later in the earthquake cycle.     

Stress transfer and nonlinear stress accumulation at subduction-type plate boundaries — Application to the Aleutians

A study of stress accumulation in seismic gaps and of stress transfer along linear plate boundaries is presented. Time-dependent reloading of plate boundaries following seismic ruptures is modeled by a modified Elsasser model of a coupled lithosphere/asthenosphere plate system. This model is applied to study a series of large earthquakes in the Aleutian Islands and the Alaska peninsula in 1938–1965. It is found that the Rat Island earthquake and the 1948 earthquake in the central Aleutians are likely to have been triggered by adjacent ruptures, in the sense that their occurrence would have come at a later time had their neighboring segments not been ruptured. Stresses in the Unalaska Gap and the Shumagin gap are at a relatively high level and these segments of the plate boundary may be expected to rupture in the near future. In general, in the ten years (about 16% of the earthquake cycle for the Aleutians) following an earthquake, the stress recovery in the rupture zone is highly nonlinear, resulting in a much more rapid stress accumulation than the linear case. Even at a later stage of an earthquake cycle, adjacent ruptures can cause an acceleration of loading rate in addition to the coseismic stress jump. A good example is the influence of the 1964 Alaska earthquake on the 1938 rupture zone. A general conclusion of this work is that long term earthquake prediction models must take into account the nonlinear stress accumulation behavior in seismic gaps. Also, we have shown the interaction of adjacent plate boundary segments, which suggests that some large earthquakes may have been triggered by nearby ruptures.     

引潮力对显著地震触发作用与大震关系的机理讨论

初步讨论了引潮力对显著地震触发作用与大震关系的机理。 结果表明, 这一机理是比较复杂的。 地震发生时水平引潮力方位与地震断层面走向接近, 可能增加断层面上的剪应力, 有利于地震的发生; 水平引潮力方位与地震主张应力轴T轴接近, 可能减小断层面上的正应力, 从而减小断层面上的摩擦力, 也会有利于地震的发生。 所讨论的3个震例中有2个共同点: 其一为大震前显著地震发生时水平引潮力方位相互比较接近; 其二为显著地震破裂面走向和大震破裂面走向基本一致。